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pi(0.04)^2cos(30)(-0.2)

Solução

π (0.04)^{2} cos (3 0^{\circ}) (- 0.2)

- \frac{3 π}{6250}

Decimal

- 0.00087 \dots

Passos da solução

18 0^{\circ} (0.04)^{2} cos (3 0^{\circ}) (- 0.2)

= 18 0^{\circ} (\frac{1}{25})^{2} cos (3 0^{\circ}) (- \frac{1}{5})

Utilizar a seguinte identidade trivial:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\circ})

cos (x)

tabela de periodicidade com ciclo de

36 0^{\circ} n

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= 18 0^{\circ} (\frac{1}{25})^{2} \frac{3}{2} (- \frac{1}{5})

Simplificar

18 0^{\circ} (\frac{1}{25})^{2} \frac{3}{2} (- \frac{1}{5}) : - \frac{3 18 0 ^{\circ}}{6250}

18 0^{\circ} (\frac{1}{25})^{2} \frac{3}{2} (- \frac{1}{5})

Remover os parênteses:

(- a) = - a

= - 18 0^{\circ} (\frac{1}{25})^{2} \frac{3}{2} \cdot \frac{1}{5}

(\frac{1}{25})^{2} = \frac{1}{2 5 ^{2}}

(\frac{1}{25})^{2}

Aplicar as propriedades dos expoentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{2 5 ^{2}}

Aplicar a regra

1^{a} = 1

1^{2} = 1

= \frac{1}{2 5 ^{2}}

= - 18 0^{\circ} \frac{1}{5} \cdot \frac{1}{2 5 ^{2}} \cdot \frac{3}{2}

Multiplicar frações:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= - \frac{1 \cdot 3 \cdot 18 0 ^{\circ}}{2 5 ^{2} \cdot 2 \cdot 5}

Multiplicar:

1 \cdot 3 \cdot 18 0^{\circ} = 318 0^{\circ}

= - \frac{3 18 0 ^{\circ}}{2 5 ^{2} \cdot 2 \cdot 5}

Multiplicar os números:

2 \cdot 5 = 10

= - \frac{3 18 0 ^{\circ}}{2 5 ^{2} \cdot 10}

10 \cdot 2 5^{2} = 6250

10 \cdot 2 5^{2}

2 5^{2} = 625

= 10 \cdot 625

Multiplicar os números:

10 \cdot 625 = 6250

= 6250

= - \frac{3 18 0 ^{\circ}}{6250}

= - \frac{3 18 0 ^{\circ}}{6250}

6 sin (3)

5 cos (18 0^{\circ})

cos (17 5^{\circ})

arccos (0.7142)

7 \cdot tan (3 5^{\circ})